1. Field of the Invention
The present invention relates to quantum information processing, and, in particular, to techniques for increasing the fidelity of teleportation and logic operations on quantum bits (qubits) represented by quantum states of single photons.
2. Description of the Related Art
Information processing using classical computers relies on physical phenomena, such as magnetic fields, voltages, and optical intensity that can be produced and measured in each of two basis states, one basis state representing a zero and another basis state representing a one. Each physical element that can achieve either of these two states represents one binary digit, called a bit. Quantum information processing uses physical elements that exhibit quantum properties that may include, not only one of the two or more basis states, but also an arbitrary superposition state of the basis states. A superposition state has some non-zero probability of being measured as one of the basis states and some non-zero probability of being measured as another of the basis states. A physical element that exhibits quantum properties for two basis states represents one quantum bit, also called a qubit. Physical elements that are suitable for representing qubits include the spins of single electrons, electron states in atoms or molecules, nuclear spins in molecules and solids, magnetic flux, spatial propagation modes of single photons, and polarizations of single photons, among others.
Logical operations performed on qubits apply not only to the basis states of those qubits but also to the superposition states of those qubits, simultaneously. Quantum computers based on logical operations on systems of qubits offer the promise of massively simultaneous processing (also called massively parallel processing) that can address problems that are considered intractable with classical information processing. Such classically intractable problems that can be addressed with quantum computers include simulation of quantum interactions, combinatorial searches of unsorted data, finding prime factors of large integers, solving for cryptographic keys used in current secure communication algorithms, and truly secure communications (also called “quantum cryptography”).
One approach uses linear interactions between single photons but relies on interferometer techniques, e.g., interference on two spatial modes of propagation for a single photon. For example, logic gates using this approach have been proposed by E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature, vol. 409, p. 49, 4 Jan. 2001 (hereinafter Knill) and by M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Physical Review A, vol. 63, 030301, 12 Feb. 2001 (hereinafter Koashi), the entire contents of each of which are hereby incorporated by reference as if fully set forth herein. These devices are called “probabilistic” logical gates because they perform the desired logical operation in response to only a fraction of the input photons. However, it can be determined when an operation is performed successfully, so that, in a separate step often called a “post selection” step or a “post-detection selection” step, output photons are blocked unless the operation is successfully performed. It has been shown that the fraction can be increased close to a value of one with sufficient numbers of components and extra photons (called “ancilla photons” or “ancilla”) in particular states.
Although the occurrence of certain failures in the Knill approach can be identified by measurements on the ancilla, devices based on the Knill approach might still benefit from the use of quantum error correction techniques. The certain failures identified are equivalent to z-measurement errors, which can be corrected using a simple two-bit concatenated code that operates even in the presence of a relatively high error rate (e.g., as described in E. Knill, R. Laflamme, and G. Milbum, quant-ph/0006120). The devices proposed in Knill also suffer from errors due to thermally induced phase shifts on the two spatial modes. The same two-bit code can be used to correct for phase-shift errors and possibly for photon losses. Other probabilistic, linear devices proposed by Koashi reduce the phase shifts by including a large number of additional components and other resources, such as sources of a large number of qubits in particular states. However, the two-bit code and the approach of Koashi have not been shown to correct for more general errors, e.g., errors that would be introduced by imperfect generation of the entangled ancilla states.
The use of more general quantum error correction approaches require a relatively low error rate, called the “error threshold” of the correction approach. For the Knill approach to reduce error rates below the error threshold of general quantum error correction, a large number of ancilla photons are needed. Knill shows that the failure probability could decrease as 1/N, where N is the number of ancilla photons, in the limit of large N. With sufficiently large N, the approach of Knill should be able to be used with general quantum error correction approaches.
However, there are several additional problems if the number N of ancilla becomes too great. One additional problem is that an increase in N involves an increase in the number of resources required in a quantum computing device to generate the increased number of ancilla. Another problem is that an increase in N increases the probability of technical errors (e.g. phase shifts, photon loss, etc.) in the logic operation using the extra ancilla along with the probability that an error will occur in the generation of one or more ancilla. Thus a point of diminishing returns may be reached where it becomes more difficult to reduce the error rate below the error threshold because the increase in the number of ancilla to reduce the intrinsic error (1/N) in the Knill approach also increases the chances of technical errors in the generation of the ancilla or in the logic device using the extra ancilla.
Based on the foregoing description, there is a clear need for techniques that increase the fidelity of quantum logic operations on qubits represented by single photons that do not suffer the deficiencies of current approaches. In particular, there is a clear need for techniques that decrease the failure rate of quantum logic operations at a rate faster than the reciprocal of the first power of the number of ancilla.
The approaches described in this section could be pursued, but are not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated herein, the approaches described in this section are not to be considered prior art to the claims in this application merely due to the presence of these approaches in this background section.